Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshe

Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method

We present a robust and scalable solver for time-harmonic Maxwell's equations for problems with large conductivity contrasts, wide range of frequencies, stretched grids and locally refined meshes. The solver is part of the fully distributed adaptive 3-D electromagnetic modelling scheme which employs the finite element method and unstructured non-conforming hexahedral meshes for spatial discretization using the open-source software deal.II. We use the complex-valued electric field formulation and split it into two real-valued equations for which we utilize an optimal block-diagonal pre-conditioner. Application of this pre-conditioner requires the solution of two smaller real-valued symmetric problems. We solve them by using either a direct solver or the conjugate gradient method pre-conditioned with the recently introduced auxiliary space technique. The auxiliary space pre-conditioner reformulates the original problem in form of several simpler ones, which are then solved using highly efficient algebraic multigrid methods. In this paper, we consider the magnetotelluric case and verify our numerical scheme by using COMMEMI 3-D models. Afterwards, we run a series of numerical experiments and demonstrate that the solver converges in a small number of iterations for a wide frequency range and variable problem sizes. The number of iterations is independent of the problem size, but exhibits a mild dependency on frequency. To test the stability of the method on locally refined meshes, we have implemented a residual-based a posteriori error estimator and compared it with uniform mesh refinement for problems up to 200 million unknowns. We test the scalability of the most time consuming parts of our code and show that they fulfill the strong scaling assumption as long as each MPI process possesses enough degrees of freedom to alleviate communication overburden. Finally, we refer back to a direct solver-based pre-conditioner and analyse its complexity in time. The results show that for multiple right-hand sides the direct solver-based pre-conditioner can still be faster for problems of medium size. On the other hand, it also shows non-linear growth in memory, whereas the auxiliary space method increases only linearly.ISSN:0956-540XISSN:1365-246

Satellite tidal magnetic signals constrain oceanic lithosphere-asthenosphere boundary

The tidal flow of electrically conductive oceans through the geomagnetic field results in the generation of secondary magnetic signals, which provide information on the subsurface structure. Data from the new generation of satellites were shown to contain magnetic signals due to tidal flow; however, there are no reports that these signals have been used to infer subsurface structure. We use satellite-detected tidal magnetic fields to image the global electrical structure of the oceanic lithosphere and upper mantle down to a depth of about 250 km. The model derived from more than 12 years of satellite data reveals a ≈72-km-thick upper resistive layer followed by a sharp increase in electrical conductivity likely associated with the lithosphere-asthenosphere boundary, which separates colder rigid oceanic plates from the ductile and hotter asthenosphere.ISSN:2375-254

Satellite Tidal Magnetic Signals Constrain Oceanic Lithosphere-Asthenosphere Boundary Earth Tomography with Tidal Magnetic Signals

The tidal flow of electrically conductive oceans through the geomagnetic field results in the generation of secondary magnetic signals, which provide information on the subsurface structure. Data from the new generation of satellites were shown to contain magnetic signals due to tidal flow; however, there are no reports that these signals have been used to infer subsurface structure. Here we use satellite-detected tidal magnetic fields to image the global electrical structure of the oceanic lithosphere and upper mantle down to a depth of about 250 km. The model derived from more than 12 years of satellite data reveals an Approximately 72 km thick upper resistive layer followed by a sharp increase in electrical conductivity likely associated with the lithosphere-asthenosphere boundary, which separates colder rigid oceanic plates from the ductile and hotter asthenosphere

Global 3-D Electrical Conductivity Model of the World Ocean and Marine Sediments

This study presents global 3-D electrical conductivity models of the world ocean and marine sediments. Electrical conductivity of the ocean was calculated by invoking the Equation of State of Seawater (TEOS-10) with temperature and salinity data retrieved from the World Ocean Atlas and a series of high-resolution regional ocean climatology data sets. The resolution of the ocean conductivity atlas varies between 0.urn:x-wiley:15252027:media:ggge22631:ggge22631-math-0001 and 0.urn:x-wiley:15252027:media:ggge22631:ggge22631-math-0002 globally. The conductivity of marine sediments was estimated by using compaction and thermal gradient models constrained by real observations on a 5-arc-minute global marine sediment thickness grid. I present numerical simulations of electromagnetic (EM) induction responses that demonstrate a significant effect of 3-D electrical conductivity of the ocean and marine sediments on EM responses for a broad range of frequencies. I show that both marine and land-based surveys designed for subsurface conductivity imaging or Space Weather modeling will benefit from inclusion of more realistic conductivity models of the ocean and seabed sediments.ISSN:1525-202

The Magnetic Signatures of the <i>M₂,</i> <i>N₂</i>, and <i>O</i>_<i>1</i>Oceanic Tides Observed in Swarm and CHAMP Satellite Magnetic Data

ISSN:0094-8276ISSN:1944-800

Exploring equivalence domain in nonlinear inverse problems using Covariance Matrix Adaption Evolution Strategy (CMAES) and random sampling

ISSN:0956-540XISSN:1365-246

Particle streak velocimetry using ensemble convolutional neural networks

ISSN:0723-4864ISSN:1432-111